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Simultaneous Equations

It’s been a while since i last wrote anything here. Which says more about how busy I’ve been than my desire to write, but I hope to start writing more regularly.

This week I was teaching simultaneous equations and a student asked a question that made me think about things so I thought i would share.

I was teaching elimination method and I had done some examples with the coefficients of y having different signs and I put one on the board with the same signs and asked the class to think how we may go about solving. One of the students in the class put uo his hand after a while and said he thought he had solved it.

5x + 4y = 13

2x + 2y = 6

I asked hime to talk us through his thinking and he said “first I multipled the bottom equation by -2”

5x + 4y = 13

-4x – 4y = -12

“then I added the equations as before”

x = 1

“Then I subbed in and solved.”

2 + 2y = 6

2y = 4

y = 2

“so the point of intersection is (1,2)”.

This wasn’t what I was expecting. I was expecting him to have spotted we could subtract instead, but this method was clearly just as correct. It wasn’t something I had considered as a method before this, but I actually really liked it as a method and it led to a good discussion with the class after another student interjected with her solution which was what I expected, to multiply by 2 and subtract.

It was a great start point to a discussion where the students were looking at the two methods, and understanding why they both worked, the link between addition of a negative and subtracting a positive and many more.

I was wondering, does anyone teach this as a method? Have you had similar discussions in your lessons? What do you think of it?

  1. March 10, 2019 at 4:47 pm

    This is interesting. I always teach subtracting first because I show something like:
    3x + y = 17
    3x + 2y = 22
    and then ask what y is. Then that leads onto discussions about how 5 is the difference between the equations and that leads onto a discussion about subtraction. Then I would bring in addition later in the same way that you had thought to bring in subtraction by presenting a different problem.
    That was the way I taught it to my 4/5 borderline class last year but then when we came back to SEs in revision and exam practice one or two of them had started using the multiplying by a negative method from their own initiative and then when they were helping their classmates solve problems THEY showed them that method and it spread through the class, becoming more popular (but they were multiplying by a negative so that they could create a subtraction, presumably because that is what I’d shown them first so it is what the default is in their minds, whereas for your pupils the default is presumably addition).
    So interesting! Thanks for sharing 🙂

    • March 10, 2019 at 5:25 pm

      That is quite interesting. I have introduced it ypur way in the past, but for the last few years I focus heavily on the “=” sign when i introduce Sim Eq. I think once they full understand what it means they can see how it moves better. In this case i don’t think it matters whether you introduce adding or subtracting first.They need to understand that the 2x + 2y and the 6 are the same thing, so you are adding/subtracting the same to each side as you would in a 2 step equation and that keeps both sides of the = the same.

  2. March 11, 2019 at 7:04 am

    I’m not a maths teacher, but this is the method I taught my son (year 9). Seemed to click for him in a way that other approaches hadn’t.

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